{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,15]],"date-time":"2024-09-15T14:23:07Z","timestamp":1726410187595},"publisher-location":"Berlin, Heidelberg","reference-count":30,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642157837"},{"type":"electronic","value":"9783642157844"}],"license":[{"start":{"date-parts":[[2010,1,1]],"date-time":"2010-01-01T00:00:00Z","timestamp":1262304000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2010]]},"DOI":"10.1007\/978-3-642-15784-4_8","type":"book-chapter","created":{"date-parts":[[2010,9,20]],"date-time":"2010-09-20T12:39:38Z","timestamp":1284986378000},"page":"115-130","source":"Crossref","is-referenced-by-count":0,"title":["Model Checking Markov Chains Using Krylov Subspace Methods: An Experience Report"],"prefix":"10.1007","author":[{"given":"Falko","family":"Dulat","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Joost-Pieter","family":"Katoen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Viet Yen","family":"Nguyen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"issue":"5","key":"8_CR1","doi-asserted-by":"publisher","first-page":"515","DOI":"10.1016\/0305-0548(93)90015-B","volume":"20","author":"H. Abdallah","year":"1993","unstructured":"Abdallah, H., Marie, R.: The uniformized power method for transient solutions of Markov processes. Computers & Operations Research\u00a020(5), 515\u2013526 (1993)","journal-title":"Computers & Operations Research"},{"issue":"6","key":"8_CR2","doi-asserted-by":"publisher","first-page":"524","DOI":"10.1109\/TSE.2003.1205180","volume":"29","author":"C. Baier","year":"2003","unstructured":"Baier, C., Haverkort, B., Hermanns, H., Katoen, J.-P.: Model-checking algorithms for continuous-time Markov chains. IEEE Trans. on Softw. Eng.\u00a029(6), 524\u2013541 (2003)","journal-title":"IEEE Trans. on Softw. Eng."},{"key":"8_CR3","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"32","DOI":"10.1007\/978-3-642-02652-2_7","volume-title":"Model Checking Software","author":"D. Bosnacki","year":"2009","unstructured":"Bosnacki, D., Edelkamp, S., Sulewski, D.: Efficient probabilistic model checking on general purpose graphics processors. In: P\u0103s\u0103reanu, C.S. (ed.) SPIN Workshop. LNCS, vol.\u00a05578, pp. 32\u201349. Springer, Heidelberg (2009)"},{"key":"8_CR4","series-title":"Lecture Notes in Bioinformatics","doi-asserted-by":"publisher","first-page":"298","DOI":"10.1007\/11885191_21","volume-title":"Computational Methods in Systems Biology","author":"H. Busch","year":"2006","unstructured":"Busch, H., Sandmann, W., Wolf, V.: A numerical aggregation algorithm for the enzyme-catalyzed substrate conversion. In: Priami, C. (ed.) CMSB 2006. LNCS (LNBI), vol.\u00a04210, pp. 298\u2013311. Springer, Heidelberg (2006)"},{"issue":"1","key":"8_CR5","first-page":"84","volume":"46","author":"J.A. Carrasco","year":"2003","unstructured":"Carrasco, J.A.: Transient analysis of rewarded continuous time Markov models by regenerative randomization with laplace transform inversion. The Conputer Journal\u00a046(1), 84\u201399 (2003)","journal-title":"The Conputer Journal"},{"key":"8_CR6","doi-asserted-by":"crossref","unstructured":"Chen, T., Han, T., Katoen, J.-P., Mereacre, A.: Quantitative model checking of continuous-time Markov chains against timed automata specification. In: LICS, pp. 309\u2013318 (2009)","DOI":"10.1109\/LICS.2009.21"},{"key":"8_CR7","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1007\/978-1-4757-4828-4_3","volume-title":"Computational Probability","author":"E. de Souza e Silva","year":"2000","unstructured":"de Souza e Silva, E., Gail, H.R.: Transient solutions for Markov chains. In: Grassmann, W. (ed.) Computational Probability, pp. 43\u201381. Kluwer Academic Publishers, Dordrecht (2000)"},{"key":"8_CR8","unstructured":"Duff, I., Grimes, R., Lewis, J.: User\u2019s guide for the Harwell-Boeing sparse matrix collection. Technical Report TR\/PA\/92\/86, CERFACS (1992)"},{"issue":"4","key":"8_CR9","doi-asserted-by":"publisher","first-page":"440","DOI":"10.1145\/42404.42409","volume":"31","author":"B.L. Fox","year":"1988","unstructured":"Fox, B.L., Glynn, P.W.: Computing Poisson probabilities. Commun. ACM\u00a031(4), 440\u2013445 (1988)","journal-title":"Commun. ACM"},{"issue":"2","key":"8_CR10","doi-asserted-by":"publisher","first-page":"215","DOI":"10.2307\/3318575","volume":"6","author":"S.T. Garren","year":"2000","unstructured":"Garren, S.T., Smith, R.L.: Estimating the second largest eigenvalue of a Markov transition matrix. Bernoulli\u00a06(2), 215\u2013242 (2000)","journal-title":"Bernoulli"},{"key":"8_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"337","DOI":"10.1007\/978-3-642-02658-4_27","volume-title":"Computer Aided Verification","author":"T.A. Henzinger","year":"2009","unstructured":"Henzinger, T.A., Mateescu, M., Wolf, V.: Sliding window abstraction for infinite Markov chains. In: Bouajjani, A., Maler, O. (eds.) Computer Aided Verification. LNCS, vol.\u00a05643, pp. 337\u2013352. Springer, Heidelberg (2009)"},{"key":"8_CR12","unstructured":"Hermanns, H., Meyer-Kayser, J., Siegle, M.: Multi terminal binary decision diagrams to represent and analyse continuous time Markov chains. In: Plateau, B., Stewart, W., Silva, M. (eds.) Proc. 3rd International Workshop on Numerical Solution of Markov Chains (NSMC 1999), pp. 188\u2013207. Prensas Universitarias de Zaragoza (1999)"},{"issue":"5","key":"8_CR13","doi-asserted-by":"publisher","first-page":"1911","DOI":"10.1137\/S0036142995280572","volume":"34","author":"M. Hochbruck","year":"1997","unstructured":"Hochbruck, M., Lubich, C.: On Krylov subspace approximations to the matrix exponential operator. SIAM on Numerical Analysis\u00a034(5), 1911\u20131925 (1997)","journal-title":"SIAM on Numerical Analysis"},{"key":"8_CR14","volume-title":"Topics in Matrix Analysis","author":"R.A. Horn","year":"1986","unstructured":"Horn, R.A., Johnson, C.R.: Topics in Matrix Analysis. Cambridge University Press, Cambridge (1986)"},{"issue":"9","key":"8_CR15","doi-asserted-by":"publisher","first-page":"1649","DOI":"10.1109\/49.62852","volume":"8","author":"O. Ibe","year":"1990","unstructured":"Ibe, O., Trivedi, K.: Stochastic Petri net models of polling systems. IEEE Journal on Selected Areas in Communications\u00a08(9), 1649\u20131657 (1990)","journal-title":"IEEE Journal on Selected Areas in Communications"},{"key":"8_CR16","doi-asserted-by":"crossref","unstructured":"Jensen, A.: Markoff chains as an aid in the study of markoff processes. In: Skand. Aktuarietidskrift, vol.\u00a036, pp. 87\u201391 (1953)","DOI":"10.1080\/03461238.1953.10419459"},{"key":"8_CR17","first-page":"301","volume-title":"QEST","author":"J.-P. Katoen","year":"2006","unstructured":"Katoen, J.-P., Zapreev, I.S.: Safe on-the-fly steady-state detection for time-bounded reachability. In: QEST, pp. 301\u2013310. IEEE CS, Los Alamitos (2006)"},{"key":"8_CR18","first-page":"167","volume-title":"Quantitative Evaluation of Systems","author":"J.-P. Katoen","year":"2009","unstructured":"Katoen, J.-P., Zapreev, I.S., Hahn, E.M., Hermanns, H., Jansen, D.N.: The ins and outs of the probabilistic model checker MRMC. In: Quantitative Evaluation of Systems, pp. 167\u2013176. IEEE CS Press, Los Alamitos (2009)"},{"key":"8_CR19","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"234","DOI":"10.1007\/11817963_23","volume-title":"Computer Aided Verification","author":"M. Kwiatkowska","year":"2006","unstructured":"Kwiatkowska, M., Norman, G., Parker, D.: Symmetry reduction for probabilistic model checking. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol.\u00a04144, pp. 234\u2013248. Springer, Heidelberg (2006)"},{"key":"8_CR20","first-page":"711","volume-title":"Dependable Systems and Networks (DSN)","author":"M. Massink","year":"2004","unstructured":"Massink, M., Katoen, J.-P., Latella, D.: Model checking dependability attributes of wireless group communication. In: Dependable Systems and Networks (DSN), pp. 711\u2013720. IEEE CS Press, Los Alamitos (2004)"},{"issue":"1","key":"8_CR21","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1137\/S00361445024180","volume":"45","author":"C. Moler","year":"2003","unstructured":"Moler, C., Van Loan, C.: Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later. SIAM Review\u00a045(1), 3\u201349 (2003)","journal-title":"SIAM Review"},{"issue":"6","key":"8_CR22","doi-asserted-by":"publisher","first-page":"395","DOI":"10.2307\/2306996","volume":"62","author":"R.F. Rinehart","year":"1955","unstructured":"Rinehart, R.F.: The equivalence of definitions of a matrix function. The American Mathematical Monthly\u00a062(6), 395\u2013414 (1955)","journal-title":"The American Mathematical Monthly"},{"issue":"1","key":"8_CR23","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1137\/0729014","volume":"29","author":"Y. Saad","year":"1992","unstructured":"Saad, Y.: Analysis of some Krylov subspace approximations to the matrix exponential operator. SIAM Journal on Numerical Analysis\u00a029(1), 209\u2013228 (1992)","journal-title":"SIAM Journal on Numerical Analysis"},{"issue":"1","key":"8_CR24","doi-asserted-by":"publisher","first-page":"130","DOI":"10.1145\/285861.285868","volume":"24","author":"R. Sidje","year":"1998","unstructured":"Sidje, R.: Expokit: a software package for computing matrix exponentials. ACM Trans. Math. Softw.\u00a024(1), 130\u2013156 (1998)","journal-title":"ACM Trans. Math. Softw."},{"key":"8_CR25","doi-asserted-by":"publisher","first-page":"345","DOI":"10.1016\/S0167-9473(98)00062-0","volume":"29","author":"R. Sidje","year":"1996","unstructured":"Sidje, R., Stewart, W.J.: A survey of methods for computing large sparse matrix exponentials arising in Markov chains. Markov Chains, Computational Statistics and Data Analysis\u00a029, 345\u2013368 (1996)","journal-title":"Markov Chains, Computational Statistics and Data Analysis"},{"key":"8_CR26","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719574","volume-title":"Numerical Linear Algebra","author":"L.N. Trefethen","year":"1997","unstructured":"Trefethen, L.N., Bau III, D.: Numerical Linear Algebra. Society for Industrial and Applied Mathematics, Philadelphia (1997)"},{"issue":"3","key":"8_CR27","doi-asserted-by":"publisher","first-page":"619","DOI":"10.1080\/15326349408807313","volume":"10","author":"A. Moorsel van","year":"1994","unstructured":"van Moorsel, A., Sanders, W.: Adaptive uniformization. Communications in Statistics - Stochastic Models\u00a010(3), 619\u2013648 (1994)","journal-title":"Communications in Statistics - Stochastic Models"},{"issue":"4","key":"8_CR28","doi-asserted-by":"publisher","first-page":"600","DOI":"10.1137\/0714039","volume":"14","author":"R.C. Ward","year":"1977","unstructured":"Ward, R.C.: Numerical computation of the matrix exponential with accuracy estimate. SIAM Journal on Numerical Analysis\u00a014(4), 600\u2013610 (1977)","journal-title":"SIAM Journal on Numerical Analysis"},{"issue":"3","key":"8_CR29","doi-asserted-by":"publisher","first-page":"511","DOI":"10.1137\/0915034","volume":"15","author":"R. Weiss","year":"1994","unstructured":"Weiss, R.: Error-minimizing Krylov subspace methods. SIAM Journal on Scientific Computing\u00a015(3), 511\u2013527 (1994)","journal-title":"SIAM Journal on Scientific Computing"},{"key":"8_CR30","unstructured":"Zapreev, I.S.: Model Checking Markov Chains: Techniques and Tools. PhD thesis, Univ. of Twente (2008)"}],"container-title":["Lecture Notes in Computer Science","Computer Performance Engineering"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-15784-4_8","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,4]],"date-time":"2019-06-04T23:00:03Z","timestamp":1559689203000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-15784-4_8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010]]},"ISBN":["9783642157837","9783642157844"],"references-count":30,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-15784-4_8","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2010]]}}}